Normal ordering and boundary conditions in open bosonic strings

Boundary conditions play a non trivial role in string theory. For instance the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end-points (corresponding to mixed boundary conditions) space time becomes non-commutative there. We show here how to build up normal ordered products for bosonic string position operators that satisfy both equations of motion and open string boundary conditions at quantum level. We also calculate the equal time commutator of these normal ordered products in the presence of antisymmetric tensor background.Comment: 7 pages no figures, References adde

Extended BRST invariance in topological Yang Mills theory revisited

Extended BRST invariance (BRST plus anti-BRST invariances) provides in principle a natural way of introducing the complete gauge fixing structure associated to a gauge field theory in the minimum representation of the algebra. However, as it happens in topological Yang Mills theory, not all gauge fixings can be obtained from a symmetrical extended BRST algebra, where antighosts belong to the same representation of the Lorentz group of the corresponding ghosts. We show here that, at non interacting level, a simple field redefinition makes it possible to start with an extended BRST algebra with symmetric ghost antighost spectrum and arrive at the gauge fixing action of topological Yang Mills theory.Comment: Interaction terms heve been included in all the calculations. Two references added. Version to be published in Phys. Rev. D. 7 pages, Latex, no figure

Symplectic Quantization of Open Strings and Noncommutativity in Branes

We show how to translate boundary conditions into constraints in the symplectic quantization method by an appropriate choice of generalized variables. This way the symplectic quantization of an open string attached to a brane in the presence of an antisymmetric background field reproduces the non commutativity of the brane coordinates.Comment: We included a comparison with previous results obtained from Dirac quantization, emphasizing the fact that in the symplectic case the boundary conditions, that lead to the non commutativity, show up from the direct application of the standard method. Version to appear in Phys. Rev.

Fractional Dirac Bracket and Quantization for Constrained Systems

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical Review

Variational procedure for higher-derivative mechanical models in a fractional integral

We present both the Lagrangian and Hamiltonian procedures to treat higher-derivative equations of motion for mechanical models by adopting the Riemann-Liouville fractional integral to formulate their respective actions. Our focus is the possible interplay between fractionality and a dynamics based on higher derivatives. We point out and discuss the efficacy and difficulties of this approach. We also contemplate physical and geometrical interpretations and present details of the inspection we carry out by considering an explicit situation, that of a higher-derivative harmonic oscillator. Additionally, we have also used a recent proposal of a variational approach with local deformed derivatives. In this context, we have derived a complete set of linear and non-linear equations for a Pais-Uhlenbeck–type oscillator